Converged Velocity Field for Rotors by a Blended Potential Flow Method

Potential-flow solutions for rotor induced flow by the He method give good convergence on the disk but can provide only a crude approximation off of the disk. The Morillo-Duffy formulation can give all three components off the disk, but the results converge poorly on the disk. Furthermore, Morillo-Duffy solutions converge very slowly for the velocity downstream in the limit as wake skew angle approaches 90° (edgewise flow). In this work, new variables––called the Nowak-He variables––are introduced that provide both the He velocity and the Morillo-Duffy velocity from a single set of states. In addition, an approximate downstream velocity field is obtained from the adjoint theorem that gives the exact downstream velocity as skew angle approaches 90°. The blending of these three velocity fields is shown to give robust and accurate convergence to the potential-flow equations at all flight conditions.